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# Programme of Course "Mathematical Economics and Finance"

DT0110

### Type of course unit:

Bachelor Degree in Mathematics curriculum Generale: Elective
Master Degree in Mathematics curriculum Generale: Elective
Master Degree in Mathematical Engineering curriculum Comune: Elective

1st semester

### Number of credits:

Master Degree in Mathematics: 6 (workload 150 hours)
Master Degree in Mathematical Engineering: 6 (workload 150 hours)
Bachelor Degree in Mathematics: 6 (workload 150 hours)

### Teachers:

Massimiliano Giuli (massimilianogiuliunivaqit)

## 1. Course Objectives

I present and organize the analytical foundations underlying modern economics and finance.

## 2. Course Contents and learning outcomes (Dublin Descriptors)

Topics of the course include:

• Sperner’s lemma
• The Knaster-Kuratowski-Mazurkiewicz lemma
• Brouwer's fixed point theorem
• Variational inequalities and equilibrium problems
• Generalized monotonicity and convexity
• Brézis-Nirenberg-Stampacchia theorem and Fan's minimax principle
• Continuity of correspondences
• Browder, Kakutani and Fan-Glicksberg fixed point theorems
• Gale-Nikaido-Debreu theorem
• Nash equilibrium of games and abstract economies
• Walrasian equilibrium of an economy
• An application to traffic network

On successful completion of this course, the student should

• Know the fundamental fixed point theorems for set-valued maps and the basic existence results for equilibrium problems and variational inequalities.
• Explain some interconnections among these various results.
• Apply this analysis to game and economic theory

## 3. Course Prerequisites

I assume familiarity with vector and topological spaces, and with the standard model of the real numbers. I assume that you know the basic facts about metric spaces, normed and seminormerd spaces, Banach and Hilbert spaces.

Language:English

## 5. Assessment Methods

Written and oral

Course information last updated on: 19 gennaio 2018, 17:31